Our experiments have been conducted on three benchmark datasets: ESOL, FreeSolv, and Lipophilicity from [1]}. They are three molecular property prediction datasets that are used to assess the performance of GNNs. Meanwhile, there are many types of GNN algorithms, but the neural fingerprint graph model (GC) [2]} has been selected because it was proposed to be used for molecular machine learning. GC exploits the neural architectures to model circular fingerprint [3]} for learning the molecular representations for prediction tasks. There are four hyperparameters selected for HPO, including \(s_b\)  (batch size), \(l_r\)  (learning rate), \(s_g\)  (the size of graph convolution layer), and \(s_f\)  (the size of fully-connect layer); the search space is constructed as follows: the range of \(s_b\)  is \(8\sim 512\)  with step size 8, the range of \(l_r\)  is \(0.0001\sim 0.0032\)  with step size 0.0001, the range of \(s_g\)  is 8 \(\sim \)  512 with step size 8, and the range of \(s_f\)  is 32 \(\sim \)  1024 with step size 32. As mentioned in Section REF , TSM requires thresholds to divide the whole search space into many subspace, and we uses the median values of \(s_b\) , \(l_r\) , \(s_g\) , and \(s_f\) , which are 256, 0.0016, 256, and 512, respectively to build the binary tree in experiments.
